Head coach Heyneke Meyer expressed relief after South Africa ended one of the most difficult weeks of his career with a 46-6 six-try, bonus-point victory over Samoa.
JP Pietersen scored a hat-trick of tries as the two-time World Cup champions responded from their shock opening Pool B loss to Japan.
Should the Springboks beat Scotland and the United States - two sides who meet in Leeds on Sunday - then they will top the pool and gain a more favourable quarter-final draw.
"It's been a tough week," Meyer said.
"I've been there (difficult times) a few times in my life. That's when I'm usually at my best and I'm usually true to myself.
"I don't want to take anything away from the players. I just said please listen to me, do whatever we do and it will be an easy game.
"That's why I coach. I'm crazy as hell. Sometimes you don't know why. It's also great to look yourself in the mirror and see how tough you are.
"We went back to what I'm good at, the players bought in and I'm thankful for the players for listening to me.
"I asked the senior players to put up their hands and they did.
"(But) we have to keep our feet on the ground and stay humble.
"(There is) still a long way to go. It's not good enough to have one performance like that."
The Springboks also scored tries through Schalk Burger, Schalk Brits and Bryan Habana, while Handre Pollard kicked 14 points.
Michael Stanley's two penalties were all Samoa could muster in reply.
"We scored six tries, but I'm proud of our defence, not to concede," Meyer added.
"Samoa's a quality side. We were maybe lucky at times. The thing I'm proudest of is the players put their bodies on the line.
"Scotland's going to be tough. Relief and just focused on the next one."
The win came at a cost with captain Jean de Villiers heading to hospital for an X-ray on his jaw.
Meyer asked "how long is the press conference?" when asked to list the wounded, with "probably five or six other players" on a "long list".
Victor Matfield praised the influence of Meyer.
Matfield said: "He brought his craziness and what he brings to the team. He was just fantastic this week, so easy to follow him if he gets into that zone.
"We're still under pressure. Whenever the Springboks are under pressure, coach Heyneke has got this story about charcoal under pressure becomes diamonds.
"We'll probably need to be better this week coming against Scotland. They're a very good team.
"It's only one game for us that matters and that's the game against Scotland."
Meyer and Matfield revealed the huge number of messages of support received by the Springboks provided huge motivation for a country where rugby has a big influence since the unifying 1995 World Cup win on home soil.
"Our country needs a lot of hope and the Springboks is the hope of the country," Meyer added.
"When the Springboks does well, the country is in a great state.
"It is pressure, it is extra pressure and the guys responded."
Samoa next play Japan, eager to respond and confident they too can progress to the last eight.
Samoa head coach Stephen Betham said: "We came here knowing it was going to be a hard road for us and it proved to be.
"We threw everything at it, but credit to South Africa, they came out firing right from the start and we found ourselves on the back foot.
"We'll head into Japan, knowing that we'll use our get out of jail free card. We're going to prepare well.
"Our pool is still wide open. It's anyone's game. We've got Japan and I'm sure Japan's ready for us as well."